The family issued a statement early on Sunday, hours after the Israeli army said it had located bodies in Gaza.
"With broken hearts, the Goldberg-Polin family is devastated to announce the death of their beloved son and brother, Hersh," it said.
"The family thanks you all for your love and support and asks for privacy at this time."
There was no immediate comment from the army, or details about the other bodies found.
The 23-year-old was among the hostages seized by militants at a music festival in southern Israel on October 7. He lost part of an arm in the attack.
Goldberg-Polin's parents became perhaps the most high-profile relatives of hostages on the international stage.
They met with US President Joe Biden, Pope Francis and others and addressed the United Nations.
They addressed a hushed hall at the Democratic National Convention on August 21, where the crowd chanted: "Bring them home".
Jon Polin and Rachel Goldberg spoke at the Democratic National Convention last month. (AP PHOTO)
A Hamas-issued video in April showing Goldberg-Polin clearly speaking under duress sparked new protests in Israel urging the government to do more to secure his and others' freedom.
The announcement is certain to put pressure on Prime Minister Benjamin Netanyahu to reach a deal to bring home remaining hostages. The Israeli leader has said military pressure is needed to win their release as cease-fire efforts falter.
Before Israel's announcement, Israel said it believed 108 hostages were still held in Gaza and about one-third of them were dead.
Meanwhile, a campaign to inoculate children in Gaza against polio and prevent the spread of the virus has begun as Palestinians in the Hamas-governed enclave and the occupied West Bank reel from Israel's military offensives.
A small number of children in Gaza received vaccine doses a day before the large-scale rollout and limited pauses in the fighting agreed to by Israel and the UN World Health Organization.
A baby was diagnosed with the first polio case in 25 years in Gaza. (AP PHOTO)
"There must be a cease-fire so that the teams can reach everyone targeted by this campaign," said Dr Yousef Abu Al-Rish, Gaza's deputy health minister, describing scenes of sewage running through crowded tent camps. Polio is spread through fecal matter.
But Israeli Prime Minister Benjamin Netanyahu's office in a statement said "Israel will allow a humanitarian corridor only" and "areas will be established that will be safe for administering the vaccines for a few hours".
Israel said the vaccination program would continue until September 9 for eight hours a day. It will allow health workers to administer vaccines with the aim of reaching some 640,000 Palestinian children.
The vaccination campaign comes after the first polio case in 25 years in Gaza was discovered this month.
Doctors concluded a 10-month-old had been partially paralysed by a mutated strain of the virus after not being vaccinated due to fighting.
Most people who contract the disease do not experience symptoms, and those who do usually recover in a week or so. But there is no cure.
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